Subgroups — C₂₃×D₁₂₈ #19155177

Order 5888.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₆₄	C₂	1	2	yes	maximal, complemented
2	C₂₃×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×D₃₂	—	2	2	no	—
4	C₂₃×C₆₄	C₂²	1	1	yes	characteristic
5	C₂₃×D₁₆	—	4	2	no	—
6	C₂₃×C₃₂	D₄	1	1	yes	characteristic
7	D₈×C₂₃	—	8	2	no	—
8	C₁₆×C₂₃	D₈	1	1	yes	characteristic
9	D₁₂₈	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	D₄×C₂₃	—	16	2	no	—
11	C₈×C₂₃	D₁₆	1	1	yes	characteristic
12	D₆₄	C₂×C₂₃	1	2	yes	complemented
13	C₁₂₈	C₂×C₂₃	1	1	yes	characteristic, complemented
14	C₂²×C₂₃	—	32	2	no	—
15	C₄×C₂₃	D₃₂	1	1	yes	characteristic
16	D₃₂	—	2	2	no	—
17	C₆₄	C₂²×C₂₃	1	1	yes	characteristic
18	C₂×C₂₃	—	64	2	no	—
19	C₂×C₂₃	D₆₄	1	1	yes	characteristic
20	D₁₆	—	4	2	no	—
21	C₃₂	D₄×C₂₃	1	1	yes	characteristic
22	C₂₃	D₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
23	D₈	—	8	2	no	—
24	C₁₆	D₈×C₂₃	1	1	yes	characteristic
25	D₄	—	16	2	no	—
26	C₈	C₂₃×D₁₆	1	1	yes	characteristic
27	C₂²	—	32	2	no	—
28	C₄	C₂₃×D₃₂	1	1	yes	characteristic
29	C₂	—	64	2	no	—
30	C₂	C₂₃×D₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₃	D₆₄
commutator, Frattini, cosocle	C₆₄	C₂²×C₂₃
LCS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₄×C₂₃ ◁ C₈×C₂₃ ◁ C₁₆×C₂₃ ◁ C₂₃×C₃₂ ◁ C₂₃×C₆₄ ◁ G

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.